Membership in Mensa requires an IQ score above 131.5. Nine candidates take IQ tests, and their summa
Question: Membership in Mensa requires an IQ score above 131.5. Nine candidates take IQ tests, and their summary results indicate that their mean IQ score is 133. (Assume IQ scores are normally distributed with a mean of 100 and a standard deviation of 15).
a. If one person is randomly selected from the population as a whole, find the probability of getting someone with an IQ score of at least 133.
b. If 9 people are randomly selected from the population as a whole, find the probability their mean IQ score is at least 133.
c. Although the summary results are available for our nine Mensa candidates, the individual IQ test scores have been lost. Can it be concluded that all nine candidates have IQ scores above 133 so that they are eligible for Mensa membership?
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